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P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
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The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
Just Opposite
A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
Age 14 to 16
Challenge Level
This problem benefits from being able to handle real cubes using multilink or similar equipment.
Some sticky labels to identify which cubes have been painted and their locations may also prove beneficial.
Just trying to justify that in theory this should also be possible is a useful little proof.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.